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2 years ago

if y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8? a. 1/9 b. 2/3 c. 54 d. 96

Mathematics

2 answers:

Lapatulllka [165]2 years ago

8 0

The value of y when x is 8 is b. 2/3

Ivahew [28]2 years ago

3 0

Answer:

The correct option is b.

Step-by-step explanation:

It is given that y varies directly as x.

$y\propto x$

$y=kx$

It is given that y is 6 when x is 72.

$6=k\times 72$

Divide both sides by 72.

$\frac{1}{12}=k$

The constant of proportionality is $\frac{1}{12}$ .

$k=\frac{y}{x}$

$\frac{1}{12}=\frac{y}{8}$

$\frac{1}{12}\times 8=y$

$\frac{2}{3}=y$

The value of y is $\frac{2}{3}$ . The correct option is b.

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The lifetime of a certain type of battery is normally distributed with mean value 15 hours and standard deviation 1 hour. There

KIM [24]

Answer:

If the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 15

Standard Deviation, σ = 1

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We are given that the distribution of lifetime is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Standard error due to sampling:

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We have to find the value of x such that the probability is 0.05

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$= 1 -P( z \leq \displaystyle\frac{x - 40}{0.5})=0.05$

$=P( z \leq \displaystyle\frac{x - 40}{0.5})=0.95$

Calculation the value from standard normal z table, we have,

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Hence, if the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

8 0

2 years ago

Please help me with this

Cerrena [4.2K]

Answer:

Yes;Each side of triangle PQR is the same length as the corresponding side of triangle STU

Step-by-step explanation:

You can observe the sides of both triangles to see if this property holds

Lets check the length of AB

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Now check the length of the corresponding side DE

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